Many applications in modern electronics require that discrete-time signals, generated using computers and digital signal processors, be converted to linear (analog) signals, e.g., for transmission as electromagnetic signals. Typically, this transformation is made using a conventional digital-to-analog converter (DAC). However, the present inventor has discovered that each of the presently existing converters exhibits shortcomings that limit overall performance at very high sample rates.
Due to parallel processing and other innovations, the digital information processing bandwidth of computers and signal processors has advanced beyond the capabilities of state-of-the art DACs. Therefore, converters with higher instantaneous bandwidth are desired. Existing solutions are limited by instantaneous bandwidth (sample rate), effective conversion resolution (accuracy), or both.
The resolution of a DAC is a measure of the precision with which a quantized signal can be transformed into a continuous-time continuously variable signal, and typically is specified as a ratio of the total signal power to the total noise and distortion power at the DAC output. This signal-to-noise-and-distortion ratio (SNDR) of a DAC is commonly expressed on a logarithmic scale in units of decibels (dB). When a discrete-time discretely variable (digital) signal is converted into a continuous-time continuously variable (analog) signal, the quality of the analog signal is corrupted by various limitations and errors introduced during the conversion process. Examples include: (1) the finite granularity of the DAC digital inputs (bit width) that produces quantization noise, (2) the imprecise (e.g., non-linear) mapping of digital inputs to corresponding discrete output voltage or current levels that introduces distortion in the form of rounding inaccuracies (errors), (3) the imperfect timing between transitions in output voltages or currents relative to transitions in digital inputs that causes noise in the form of sampling jitter, and (4) the thermal noise associated with active devices (e.g., switches and amplifiers) that couples onto the DAC output. High-resolution converters transform discrete signals into continuously variable signals using a rounding operation with finer granularity and more-linear mapping of digital inputs to output voltage and current. Instantaneous conversion bandwidth is limited by the Nyquist criterion to a theoretical maximum of one-half the converter sample rate (the Nyquist limit). However, high-resolution conversion (of ≧10 bits) conventionally has been limited to instantaneous bandwidths of about a few gigahertz (GHz) or less.
Converters that quantize signals at a sample rate (fS) that is at or slightly above a frequency equal to twice the signal bandwidth (fB) with several or many bits of resolution are conventionally known as Nyquist-rate converters. Prior-art Nyquist-rate converter architectures include those implemented using resistor ladder networks (e.g., R-2R networks), or those employing switched current/voltage sources with unary (i.e., equal) weighting or binary weighting. A conventional resistor-ladder DAC, such as that shown in FIG. 1A, generates a variable output voltage equal to the binary-weighted sum of multiple, two-level (i.e., digital) inputs. The voltage summation operation is performed using a network of resistors, having appropriately weighted resistance (i.e., a binary-weighted resistor ladder). The voltage at the resistor network output sometimes is buffered and/or sometimes is smoothed, using an analog low-pass filter, to produce a continuously variable signal. An alternative DAC structure is illustrated in FIG. 1B, which instead of a resistor ladder network, uses a switched bank of current sources to generate a variable output current equal to the binary-weighted sum of digital inputs. As shown in FIG. 1B, the output current sometimes is converted to a proportional output voltage using a transimpedance amplifier (i.e., a current-to-voltage converter).
Conventional Nyquist converters potentially can achieve very high instantaneous bandwidths, but as discussed in greater detail below, the present inventor has discovered that component mismatches in the resistor ladder network, or in the switched current sources, can introduce rounding errors that significantly limit attainable resolution. In addition, the resolution of conventional Nyquist converters is limited by other practical implementation impairments such as sampling jitter and thermal noise. Although Nyquist converters potentially could realize high resolution at instantaneous bandwidths greater than 10 GHz in theory, due to the foregoing problems, this potential has been unrealized in conventional Nyquist converters.
Another conventional approach that attempts to reduce quantization noise and errors uses an oversampling technique. A conventional Nyquist converter transforms each digital input into a single proportional output sample (i.e., voltage or current). Conventional oversampling converters first transform each digital input into sequence of pseudorandom, two-valued samples (i.e., a positive value or a negative value), such that the average of this two-valued, pseudorandom sequence is proportional to the digital input. Therefore, oversampling converters generate coarse analog voltage or current outputs at a rate (i.e., fS) that is much higher than twice the input signal bandwidth (i.e., fS>>fB), where N=½·fS/fB is conventionally referred to as the oversampling ratio of the converter. A continuously variable output that is proportional to the digital inputs is produced from the two-valued, pseudorandom output sequence using a low-pass filtering operation that effectively averages the output samples. Although this averaging process reduces the bandwidth of the oversampling converter, it has the benefit of improving the converter resolution by mitigating quantization noise (i.e., the noise introduced by using only two values to represent a continuously variable signal) and errors resulting from component mismatches, sampling jitter, and thermal noise. The extent of this benefit is directly related to the output sample rate fS (i.e., benefit increases as sample rate increases) and is conventionally enhanced using oversampling in conjunction with a noise-shaping operation that ideally attenuates quantization noise and errors in the signal bandwidth, without also attenuating the signal itself. Through a quantization noise-shaping operation and subsequent low-pass filtering (i.e., output averaging), oversampling converters transform a high-rate intermediate signal having low resolution into a relatively low bandwidth output signal having improved resolution.
FIGS. 2A&B illustrate block diagrams of conventional, low-pass oversampling converters 5A and 5B, respectively. A typical conventional oversampling converter employs an up sampling operation 6, generally consisting of upsampling 6A by the converter oversampling ratio N followed by interpolation (low-pass) filtering 6B, and uses a delta-sigma (ΔΣ) modulator 7A&B to shape or color quantization noise. As the name implies, a delta-sigma modulator 7A&B shapes the noise that will be introduced by two-level quantizer 10 by performing a difference operation 8 (i.e., delta) and an integration operation 13A&B (i.e., sigma), e.g.,
      I    ⁡          (      z      )        =            1              1        -                  z                      -            1                                .  The converter 5A, shown in FIG. 2A, uses what is conventionally referred to as an interpolative ΔΣ modulator 7A. An alternative ΔΣ modulator 7B having the error-feedback structure shown in FIG. 2B is used in converter 5B. See D. Anastassiou “Error Diffusion Coding in A/D Conversion,” IEEE Transactions on Circuits and Systems, Vol. 36, 1989. Generally speaking, the delta-sigma modulator processes the signal with one transfer function (STF) and the quantization noise with a different transfer function (NTF). Conventional transfer functions (i.e., after accounting for the implicit delay of the two-level quantizer 10) are of the form STF(z)=z−1 and NTF(z)=(1−z−1)P, where z−1 represents a unit delay equal to TCLK=1/fCLK, and P is called the order of the modulator or noise-shaped response. The STF frequency response 30 and NTF frequency response 32 for a delta sigma modulator with P=1 are shown in FIG. 2C. For both circuits 5A&B, the output sample rate fS, and therefore the converter oversampling ratio N, is determined by the clock frequency fCLK of the delta-sigma modulator 7A&B (i.e., shown as the input clock to the two-level quantizer 10 in FIGS. 2A&B).
The delta-sigma converters 5A&B illustrated in FIGS. 2A&B are conventionally known as low-pass, delta-sigma converters. A variation on the conventional low-pass converter employs bandpass delta-sigma modulators to allow conversion of narrowband signals that are centered at frequencies above zero. An exemplary bandpass oversampling converter 40A, illustrated in FIG. 3A, includes a bandpass delta-sigma modulator 42 that shapes noise from two-level quantizer 10 by performing a difference operation 8 (i.e., delta) and an integration operation 13C (i.e., sigma), respectively, where
      H    ⁡          (      z      )        =      -                            z                      -            1                                    1          +                      z                          -              2                                          .      The conventional bandpass ΔΣ modulator, shown in FIG. 3A, is considered second-order (i.e., P=2) and, after accounting for the implicit delay of the two-level quantizer 10, has a STF(z)=z−1 and a NTF(z)=1+z−2, where z−1 represents a unit delay equal to TCLK. The noise transfer function (NTF) of a real bandpass delta-sigma modulator is at minimum a second-order response. Like the low-pass version, the bandpass ΔΣ modulator has a signal response 70, shown in FIG. 3B, that is different from its quantization noise response 71. As shown in FIG. 3B, the bandpass modulator of FIG. 3A has a NTF with a minimum 72 at the center of the converter Nyquist bandwidth (i.e., ¼·fS). After two-level quantization 10, filtering 43 of quantization noise, similar to that performed in the standard conventional low-pass oversampling converter (e.g., either of converters 5A&B) is performed. In FIG. 3A, it is assumed that the input data (i.e., digital input) rate is equal to the converter output sample rate fCLK, and therefore, an upsampling operation is not included. However, in cases where the input data rate is lower than the converter output sample rate fCLK, an upsampling operation would be included.
The present inventor has discovered that conventional low-pass ΔΣ converters, as illustrated in FIGS. 2A&B, and conventional bandpass ΔΣ converters, as illustrated in FIG. 3A, have several disadvantages that limit their utility in applications requiring very high instantaneous bandwidth and high resolution. These disadvantages, which are discussed in greater detail in the Description of the Preferred Embodiment(s) section, include: (1) conversion bandwidth that is limited by the narrow low-pass or narrow bandpass filtering operations used to attenuate shaped quantization noise and errors, (2) resolution (SNDR) that is limited by the clock frequency fCLK of the delta-sigma modulator (i.e., the clock frequency of a two-level quantizer), and (3) resolution that is limited by the low-order noise-shaped response (i.e., generally second-order for bandpass modulators) needed for stable operation with two-level quantizers. Because of these disadvantages, the resolution of conventional oversampling converters cannot be increased without: (1) reducing bandwidth to improve the quantization noise attenuation of the output (smoothing) filters, or (2) increasing the converter sample rate by using higher-speed circuits since high-order modulators are unstable with two-level quantization. In addition, conventional oversampling converters employ delta-sigma modulator structures that do not provide a means of dynamically varying, or re-programming, the frequency (fnotch) at which the quantization noise frequency response is a minimum. However, the present inventor has discovered that such a feature can be advantageous in multi-mode applications (e.g., frequency synthesizers and tunable radios) where, depending on its programming, a single converter preferably can operate on different (multiple) frequency bands.